Using the vegetable peeler, peel the potatoes. Rinse under cold running water and then place in a bowl filled with cold water to cover.

Working with one potato at a time and using the chef's knife, shape the potatoes into even cylinders. Then, using the mandoline, cut each potato crosswise into 2-millimeter (1/16-inch-thick slices. Place the slices in the stainless steel bowl, add half of the clarified butter, and toss to coat.

Preheat the oven to 204 degrees C (400 degrees F).

Heat a medium, ovenproof saute pan over very low heat. Using a pastry brush, lightly coat the bottom of the pan with clarified butter.

Arrange a layer of potatoes in slightly overlapping concentric circles over the bottom of the pan.

Drizzle with clarified butter and season with salt and pepper to taste. Continue making and seasoning layers until you have a cake about 4 centimeters (1-1/2 inches) deep.

Raise the heat to medium to briefly sear the bottom. This will prevent the potatoes from sticking to the pan while baking.

Cover the pan and transfer it to the oven. Bake for 20 minutes.

Uncover, drain, and flip the cake. Pat it down into the pan and continue to bake, uncovered, for about 20 minutes or until cooked through, crisp, and golden brown.

Remove the potato cake from the oven and carefully drain off excess butter.